We mostly use S3 for storage of compliance documents, cloud formation scripts, heavy media files and other materials which need to preserve but used infrequently. We also host some of the static webpages which are just a navigator to the documents.
One of the other most prominent use which we do with S3 is to transfer large files. With strict IMA policies, we can make sure of proper access to these files. While we use other AWS services like EC2 to host machine for any computation purpose, we need to store interim results and final results. We store these results to S3 and kill the EC2 instance.
Also, we have scripts written for transferring S3 objects (not used for more than 2 years) to Glacier to minimize cost factor.